Methods of controlling properties in multimodal systems

ABSTRACT

The invention is directed to a polymerization system and method of controlling resin properties during the production of bimodal and multimodal polymer compositions using at least one manipulated variable to minimize dynamic deviations from polymer characteristics. In particular embodiments, the method of control includes determining a property of the resin based on a current and/or previous values or estimates or process variables or polymer characteristics. In this manner the control actions serve to reduce process upsets or facilitate in transitioning to a new product or grade to reduce the amount of off-grade resin material produced during transition or during steady state manufacture.

PRIOR RELATED APPLICATIONS

This application is a 371 National Stage Application of InternationalApplication No. PCT/US06/38649 filed on Sep. 21, 2006 entitled “METHODOF CONTROLLING PROPERTIES IN MULTIMODAL SYSTEMS,” the teachings of whichare incorporated by reference herein as if reproduced in fullhereinbelow.

FEDERALLY SPONSORED RESEARCH STATEMENT

Not applicable.

REFERENCE TO MICROFICHE APPENDIX

Not applicable.

FIELD OF THE INVENTION

The invention relates generally to polymerization systems and methods ofcontrolling olefin polymerization processes. More particularly, themethods are related to control methods that offset dynamic interactionsin systems having two or more components.

BACKGROUND OF THE INVENTION

Changing from one grade of polymer to another requires a transitionperiod for a polymerization reactor to switch over to new resinspecifications and corresponding process conditions such as reactiontemperature, reactants and reactant ratios. During the transition fromone product to another, off-grade polymer material is produced that doesnot have the desired resin flow property (e.g., melt index), density, orother property of either the initial product or the desired targetproduct. In addition, a polymerization reaction operating under “steadystate” conditions can encounter variations that can result in theproduction of off-grade polymer material that can lead to loss ofrevenue and reactor shutdown. Since off-grade polymer material presentsan economic loss, it is desirable, to minimize the length of time areactor produces such material and the amount of material that isproduced.

A number of methods have been described to reduce transient, off-gradepolymer material. Such methods have involved feeding a polymerizationretarder or catalyst poison (e.g., CO₂, O₂) into the reactor, adjustingreaction gas composition, temperature and possibly pressure to newvalues, removing reactant gases from the reactor, reducing the catalystfeed rate, and/or adding a nonreactive gas such as nitrogen, among otherremedial actions.

Despite existing approaches to limit off-grade material, there is acontinuing need and desire to provide a more effective and efficientprocess to reduce the amount of off-grade polymer material producedduring the transition to a new product or as a result of a fluctuationduring steady state manufacture.

SUMMARY OF THE INVENTION

The invention is directed to a polymerization system and method ofcontrolling resin properties during the production of bimodal andmultimodal polymer compositions by manipulating one or several processvariables to minimize dynamic deviations from desired polymercharacteristics. In particular embodiments, the method of controlincludes determining a property of the resin based on a current and/orprevious values or estimates or process variables or polymercharacteristics. In this manner the control actions serve to reduceprocess upsets or facilitate in transitioning to a new product or gradeto reduce the amount of off-grade resin material produced duringtransition or during steady state manufacture.

Thus, in one aspect embodiments of the invention prove a method ofcontrolling a process for producing a polymer in at least one reactor.Embodiments of the method include (a) calculating a first value of atleast one property of a first polymer component using a mathematicalmodel for the first polymer component produced by a first catalyst orunder a first set of reaction conditions; (b) calculating a second valueof the at least one property of a second polymer component using amathematical model for the second polymer component produced by a secondcatalyst or under a first set of reaction conditions (c) determining therelative rate of production of the first and second polymer components;(d) calculating a bulk average value of the at least one property usinga mathematical model for the bulk averaged composition; (e) adjustingone or more reaction conditions thereby effecting an instantaneous valueof the at least one property of at least one of the first or secondpolymer components or effecting the production rate of at least one ofthe first or second polymer components to move the bulk average valuetoward a desired set point value.

Some embodiments of the method optionally include determining a bias orupdate factor from estimated or calculated process and resin conditionsand an independent laboratory or instrument measurement. In some suchembodiments, the first value of the at least one property is aninstantaneous value. More particularly some methods also includeoptionally adjusting the mathematical model for the first polymercomponent using the update factor determined or derived from theempirical data. In some embodiments, the second value of the at leastone property is an instantaneous value. Where the second value of the atleast one property is an instantaneous value, some methods includeoptionally adjusting the mathematical model for the second polymercomponent using the update factor determined or derived from theempirical data.

Particular embodiments of the method include optionally adjusting themathematical model for the production rate using the update factor tocorrelate properties with empirical data. Other embodiments includeoptionally adjusting the mathematical model for the bulk averaged valueof the at least one property using the update factor to correlate thebulk averaged value with empirical data. In other embodiments both themodels for the production rate and the bulk averaged value of the atleast one property are adjusted. In a particular embodiment, the updatefactor either adjusts the instantaneous model or the bulk average valueby applying the update factor to the mixing rule model.

In another aspect, embodiments of the invention are directed to a methodof controlling a process for producing a polymer composition thatincludes (a) determining an existing volume of a polymer composition;(b) calculating a first instantaneous value of a property and productionrate of a first polymer component using a mathematical model at a firsttime; (c) calculating an second instantaneous value of the property andproduction rate of a second polymer component using a mathematical modelat a first time; (d) calculating a bed average value of the property ofpolymer composition comprising the first polymer component and thesecond polymer component from the first and second instantaneous valuescalculated in (a), (b), and the existing volume based on a set of mixingrules at the first time, t₁; and (e) implementing a control action tomove the value of the bed average property toward a desired value of thebed average property.

In some embodiments, the control action includes affecting theinstantaneous value of the property of the first polymer componentand/or affecting the instantaneous value of the property of the secondpolymer component. Some embodiments include a control action thataffects the relative production rates of at least one of the first orsecond polymer components.

Where the bed average property is determined or estimated, calculatingthe bed averaged value of the property may be achieved by any suitablemethod. One such method uses a mixing rule according to the followingformula:

${\hat{P}}_{{bulk},k}^{- \frac{1}{b}} = \frac{{R_{1,k}{\hat{P}}_{1,k}^{- \frac{1}{b}}} + {f_{k}R_{2,k}{\hat{P}}_{2,k}^{- \frac{1}{b}}} + {\frac{V_{k - 1}}{\Delta\; t}{\hat{P}}_{{bulk},{k - 1}}^{{cor}^{- \frac{1}{b}}}}}{\frac{V_{k}}{\Delta\; t} + R_{{total},k}}$

-   -   where:        -   {circumflex over (P)}_(1,k)=Instantaneous Property of first            value at time k        -   {circumflex over (P)}_(2,k)=Instantaneous Property of second            value at time k        -   {circumflex over (P)}_(bulk,k−1) ^(cor)=Corrected bulk            property at time k−1        -   {circumflex over (P)}_(bulk,k)=Bulk property at time k        -   R_(1,k)=Production rate of first value at time k        -   R_(2,k)=Production rate of second value at time k        -   R_(total,k)=Total rate discharged        -   f_(k)=Model update factor at time k        -   V_(k−1)=Volume of total polymer at time k−1        -   V_(k)=Volume of total polymer at time k        -   Δt=Calculation interval        -   b=Mixing coefficient

The methods described herein may be applied in systems wherein the firstand second polymer components are produced by a single catalyst systemin a multiple reactor system. In other embodiments, the first and secondpolymer components are produced by a mixed catalyst system in a singlereactor. In still other embodiments, the first component is produced bya first catalyst and the second polymer component is produced by asecond catalyst.

BRIEF DESCRIPTION OF THE DRAWINGS

The FIGURE illustrates a process control scheme described herein.

DESCRIPTION OF EMBODIMENTS OF THE INVENTION

In the following description, all numbers disclosed herein areapproximate values, regardless whether the word “about” or “approximate”is used in connection therewith. They may vary by 1%, 2%, 5%, andsometimes, 10 to 20%. Whenever a numerical range with a lower limit,R^(L) and an upper limit, R^(U), is disclosed, any number falling withinthe range is specifically disclosed. In particular, the followingnumbers within the range are specifically disclosed:R=R^(L)+k*(R^(U)−R^(L)), wherein k is a variable ranging from 1% to 100%with a 1% increment, i.e., k is 1%, 2%, 3%, 4%, 5%, . . . , 50%, 51%,52%, . . . , 95%, 96%, 97%, 98%, 99%, or 100%. Moreover, any numericalrange defined by two R numbers as defined in the above is alsospecifically disclosed.

The term catalyst as used herein generally refers to a catalytic sitewhere polymerization occurs or to a composition known to effect thepolymerization of olefins. In some embodiments a composition having twoor more catalytic sites is used. In other embodiments, two or moresingle-site catalysts are used.

The methods described herein are generally applicable to processeswherein there is a property difference between two components of theoverall composition. Suitable properties that are modeled includeproperties related to molecular weight distribution. In particularembodiments, the first and second properties relate to the melt index orflow index. In other embodiments, to the first and second properties arelong or short chain branching frequency or density. In otherembodiments, the modeled properties may be hexane extractables. Inembodiments, where the invention is applied to polypropylene productionprocesses, suitable properties include xylene solubles, ethylenecontent, and rubber content.

The methods described herein are generally useful for a variety ofreactor system configurations. Some methods may be used in a singlereactor system employing a multiple site catalyst. In other embodiments,the methods may be used to control a single reactor with two or moresingle site catalysts. In still other embodiments, the methods describedherein can be applied to multiple reactor systems including serial andparallel reactor designs.

In the following description, a two-reactor system is used to exemplifythe particular features of embodiments of the invention. Nevertheless,the skilled artisan readily appreciates that the methods describedherein can be applied more generally to multi-reactor systems, systemsthat make more than two components, and systems using two or morecatalysts. The skilled artisan can apply these following concepts alsoto a single reactor system using dual-site or multi-site catalysts orprocesses using two or more distinct catalysts or catalyst compositions.

Embodiments of the invention are carried by a controller suitable formultimodal resin control. Embodiments of the control employ an updatefactor f_(k) related to the second reactor. This term may be used tocorrect or update the model based on the resin in the second reactor. Insome embodiments, the update factor is determined by empiricalmeasurement using laboratory data and modeled resin properties. In thisway, embodiments of the invention provide a control scheme thataddresses inherent nonlinearities in the multimodal systems.

An exemplary embodiment of a control strategy 100 is now described withreference to the FIGURE. Adjusting one or more reaction conditions isaccomplished using a trajectory generator 101. Typically, set pointinformation is supplied to trajectory generator 101 and the set pointtrajectory is calculated.

${af}_{k} = \frac{E_{k}^{SP}}{{\Delta\; t} + E_{k}^{SP}}$

-   -   where:        -   af_(k)=Tuning factor for the property at time k        -   E_(k) ^(SP)=Set point tuning time constant for the property            at time k        -   Δt=Time between iterations

Next, the set point trajectory at time k+1 is calculated.TR _(k+1) ^(SP) =af _(k)(TR _(k) ^(SP))+(1−af _(k)){circumflex over (P)}_(k) ^(SP)

-   -   where:        -   TR_(k+1) ^(SP)=Resin property set point trajectory at time            k+1        -   af_(k)=Tuning factor for the property at time k        -   TR_(k) ^(SP)=Resin property set point trajectory at time k        -   {circumflex over (P)}_(k) ^(SP)=Property set point

The feedback trajectory outputs 102 are calculated using the followingequations.

${Yd}_{k + 1}^{FB} = \frac{\left( {{\hat{P}}_{{bulk},k}^{cor} - {TR}_{k}^{SP}} \right)}{1 + \frac{\Delta\; t}{E_{k}^{FB}}}$

-   -   where:        -   Yd_(k+1) ^(FB)=Feedback trajectory at time k+1        -   {circumflex over (P)}_(bulk,k) ^(cor)=Modeled property at            time k, corrected for any lab samples        -   TR_(k) ^(SP)=Resin property set point trajectory at time k        -   E_(k) ^(FB)=Feed back tuning time constant for the property            at time k        -   Δt=Time between iterations

Other embodiments include one or more of the following features. Someembodiments of the control methodology of the invention include feedforward control using feed forward inputs 103. This control applies aknown change to the model bias across a transition at the start of thetransition to allow better prediction and control. Some methods includeadjusting the amount of error used in correcting the modeled bed averagebias based on the expected variation of the lab measurement. Anotherfeature of some embodiments of the invention is constraining themanipulated variable calculated by applying a ramp rate (both up anddown) and upper and lower limits. Some embodiments include implementingthe tuning constant such that a tuning constant of zero means thecontroller is shooting for the steady state target value, a positivetuning constant implements an overshoot or more aggressive control, anda negative value implements an undershoot or less aggressive control. Insome embodiments, separate tuning is used for transitions and steadystate. This separate tuning can be achieved by having a master recipethat is used during steady state operation and a transition recipe thatis used during transitions. Another feature that can be included isincluding time delay factors and data filtering capabilities for theinputs that are used in the control and property prediction. Wheredesired, the control can be enhanced by using logic based or batchcontrollers in addition to the continuous control described above. Anexample of a batch control would be a separate controller that wouldopen a vent if the hydrogen to ethylene ratio would get too high inorder to make it fall faster. In particular embodiments, the resultingintermediate control and final control actions are limited byconstraints of the system. For example, a sticking temperatureconstraint that will determine the temperature where resin starts tobecome sticky resulting in continuity problems or flowability problemsof the resin could be calculated and the temperature recommended by thecontinuous controller would be constrained if it was above this stickingtemperature. Other constraints include user defined limits.

With respect to resin properties, calculating the first and secondvalues of the at least one resin property is accomplished through amathematical model relating catalyst kinetics and other properties toreaction conditions. Typically, in calculating the first and secondvalues, the instantaneous property is calculated using the nonlinearresin property models 104 for each modal component and the conditionspresent at time k:{circumflex over (P)} _(i,k) ^(I) =f(uc,a _(j) ,α _(l,k))

-   -   where:        -   {circumflex over (P)}_(i,k) ^(I)=Instantaneous resin            property i at time k        -   α_(l,k)=measured process variable l at time k        -   a_(j)=Model equation constant j        -   uc=Update constant or bias to model based on lab results

Calculating the bulk average value of the at least one property is alsoaccomplished through a mathematical model. Preferred models use a mixingrule equation, instantaneous conditions, process conditions, and thebed-average properties at the previous iteration (time k−1). While anysuitable mixing rule may be used, particularly useful mixing rulesshould be stable at boundary conditions and over a wide range of reactorconditions, be time sensitive, and be suitable for use in calculatingthe control action so the control action is aware of the time dependentnature of the system. In some embodiments, a mixing rule according tothe following equation is used:

${\hat{P}}_{{bulk},k}^{- \frac{1}{b}} = \frac{{R_{1,k}{\hat{P}}_{1,k}^{- \frac{1}{b}}} + {f_{k}R_{2,k}{\hat{P}}_{2,k}^{- \frac{1}{b}}} + {\frac{V_{k - 1}}{\Delta\; t}{\hat{P}}_{{bulk},{k - 1}}^{{cor}^{- \frac{1}{b}}}}}{\frac{V_{k}}{\Delta\; t} + R_{{total},k}}$

-   -   where:        -   {circumflex over (P)}_(1,k)=Instantaneous Property of first            value (from reactor 1) at time k        -   {circumflex over (P)}_(2,k)=Instantaneous Property of second            value (from reactor 2) at time k        -   {circumflex over (P)}_(bulk,k−1) ^(cor)=Corrected bulk            property (from reactor 2) at bulk k−1        -   {circumflex over (P)}_(bulk,k)=Bulk property (from reactor            2) at time ‘k’        -   R_(1,k)=Production rate of first value (from reactor 1) at            time k        -   R_(2,k)=Production rate of second value (from reactor 2) at            time k        -   R_(total,k)=Total rate discharged        -   f_(k)=Model update factor at time k        -   V_(k−1)=Volume of total polymer at time k−1        -   V_(k)=Volume of total polymer at time k        -   Δt=Calculation interval        -   b=Mixing coefficient

One feature of this mixing rule is that the model update factor f_(k) isrelated to the properties and production rate of the second reactor.This is important because determining, either by measuring or modeling,the second reactor product is inherently more difficult. Therefore, itis beneficial to apply the correction at this point.

In control calculations, the results of trajectory generatorcalculations are used as input to the control calculations 104, wherethe manipulated variable set points are determined and passed to thebasic controller 105. For the case when the modal component productionrate is being used to control the resin property the following equationis used:

$R_{2,{k + 1}}^{SP} = \frac{{R_{1,k}\left( {{\hat{P}}_{1,k}^{- \frac{1}{b}} - {Yd}_{k + 1}^{- \frac{1}{b}}} \right)} + {\frac{V_{k}}{\Delta\; t}\left( {{\hat{P}}_{{bulk},{k - 1}}^{{cor}^{- \frac{1}{b}}} - {Yd}_{k + 1}^{- \frac{1}{b}}} \right)}}{{Yd}_{k + 1}^{- \frac{1}{b}} - {f_{k}{\hat{P}}_{2,k}^{- \frac{1}{b}}}}$

-   -   where:        -   R_(2,k+1) ^(SP)=Production rate set point of second value            (from reactor 2) at time k        -   R_(1,k)=Production rate of first value (from reactor 1) at            time k        -   {circumflex over (P)}_(1,k)=Instantaneous Property of first            value (from reactor 1) at time k        -   Yd_(k+1)=Final trajectory at time k+1        -   V_(k)=Volume of total polymer at time k        -   Δt=Calculation interval        -   {circumflex over (P)}_(bulk,k−1) ^(cor)=Corrected bulk            property (from reactor 2) at time k−1        -   {circumflex over (P)}_(2,k)=Instantaneous Property of second            value (from reactor 2) at time k        -   f_(k)=Model update factor for second reactor properties at            time k        -   b=Mixing coefficient

For the case when a different reactor control variable is being used tocontrol the resin, the target instantaneous property is firstcalculated.

${\hat{P}}_{2,{k + 1}}^{{SP}^{- \frac{1}{b}}} = \frac{{{Yd}_{k + 1}^{- \frac{1}{b}}\left( {\frac{V_{k}}{\Delta\; t} + R_{1,k} + R_{2,k}} \right)} - {R_{1,k}{\hat{P}}_{1,k}^{- \frac{1}{b}}} - {\frac{V_{k - 1}}{\Delta\; t}{\hat{P}}_{{bulk},{k - 1}}^{{cor}^{- \frac{1}{b}}}}}{f_{k}R_{2,k}}$

-   -   where:        -   {circumflex over (P)}_(2,k+1) ^(SP)=Instantaneous property            set point of second value (reactor 2) at time k+1        -   Yd_(k+1)=Final trajectory at time k+1        -   V_(k)=Volume of total polymer (in reactor 2) at time k        -   V_(k−1)=Volume of total polymer (in reactor 2) at time k−1        -   Δt=Calculation interval        -   R_(1,k)=Production rate of first value (from reactor 1) at            time k        -   R_(2,k)=Production rate of second value (from reactor 2) at            time k        -   {circumflex over (P)}_(1,k)=Instantaneous Property of first            value (from reactor 1) at time        -   f_(k)=Model update factor for second reactor properties at            time k        -   {circumflex over (P)}_(bulk,k−1) ^(cor)=Corrected bulk            property (from reactor 2) at time k−1

After the instantaneous resin property has been calculated, the specificresin property model is inverted to determine the manipulated variableset point. In cases when multiple properties are being controlled thecontroller decouples conflicting control action.

In particular embodiments of the control methodology, the methoddetermines whether or not the models used to calculate resin propertiesrequire any biasing or updating as a result of available lab samples oron line measurements. Optionally, where updating is used then it shouldbe calculated first. This bias or update constant is based on acomparison of the modeled properties calculated as well lab or empiricalresults obtained from the process 106 of the FIGURE. The data from theprocess 106 is compared to the modeled or expected resin properties 107.The difference, or a useful derivative thereof, is determined at 108,preferably iteratively, in control scheme 100. An error or difference orfraction of a difference between the process data and the expected valueand is used in determining the feedback control trajectory 102. Onemethod of determining a bias or update constant is to calculate acorrected modeled bed average property in the second reactor at the timeof the lab sample. The bias or update constant can be calculatedaccording to the equation:{circumflex over (P)} _(bulk,ts) ^(cor) ={circumflex over (P)}_(bulk,ts) +ΔE

-   -   where:        -   {circumflex over (P)}_(bulk,ts)=The modeled bulk property at            sample time ts        -   ΔE=amount of error to be used in updating model.        -   {circumflex over (P)}_(bulk,ts) ^(cor)=Corrected bulk            property at sample time ts

In the simplest case the amount of error is the difference between themodel and lab. In a different embodiment the error can be a fraction ofthe difference between the model and the lab

In the case where production rate for one of the modal components willbe used to control a resin property, an estimator 109 can be used to thecalculate the f_(k) term.

Information measured from the process 10 in the FIGURE is also used inthe calculation. The f_(k) term is calculated using the followingequation.

${\Delta\; f_{ts}} = \frac{\left\lbrack {\left( {\hat{P}}_{{bulk},{ts}}^{cor} \right)^{- \frac{1}{b}} - \left( {\hat{P}}_{{bulk},{ts}} \right)^{- \frac{1}{b}}} \right\rbrack\left( {R_{1,{ts}} + R_{2,{ts}}} \right)}{R_{2,{ts}}{\hat{P}}_{2,{ts}}^{- \frac{1}{b}}}$

-   -   where:        -   Δf_(ts)=The change in the model update factor for second            reactor property at the time of the sample ts        -   {circumflex over (P)}_(bulk,ts) ^(cor)=Corrected bulk            property at sample time ts        -   {circumflex over (P)}_(bulk,ts)=Bulk property at sample time            ts        -   {circumflex over (P)}_(2,ts)=Instantaneous property of            second value (from reactor 2) at time ts        -   R_(1,ts)=Production rate of first value (from reactor 1) at            sample time ts        -   R_(2,ts)=Production rate of second value (from reactor 2) at            sample time ts

In the case where other process conditions will be manipulated tocontrol reactor properties an estimator can also be implemented usingthe following methodology. In these cases the update constant term inmodal component instantaneous property term is updated. In order tocalculate the new update constant the following series of equations isused.

${\hat{P}}_{2,{ts}}^{cor} = \left( {\frac{\left\lbrack {\left( {\hat{P}}_{{bulk},{ts}}^{cor} \right)^{- \frac{1}{b}} - \left( {\hat{P}}_{{bulk},{ts}} \right)^{- \frac{1}{b}}} \right\rbrack\left( {R_{1,{ts}} + R_{2,{ts}}} \right)}{R_{2,{ts}}f_{ts}} + {\hat{P}}_{2,{ts}}^{- \frac{1}{b}}} \right)^{- b}$UC_(ts)^(cor) = g(P̂_(bulk, ts)^(cor)) − h(T_(ts), P_(ts), ratio⋅_(ts)..)

-   -   where:        -   {circumflex over (P)}_(2,ts) ^(cor)=Corrected instantaneous            property of second value (from reactor 2) at time ts        -   {circumflex over (P)}_(bulk,ts) ^(cor)=Corrected bulk            property at sample time ts        -   {circumflex over (P)}_(bulk,ts)=Bulk property at sample time            ts        -   R_(1,ts)=Production rate of first value (from reactor 1) at            sample time ts        -   R_(2,ts)=Production rate of second value (from reactor 2) at            sample time ts        -   f_(ts)=Model update factor for second reactor properties at            sample time ts        -   {circumflex over (P)}_(2,ts)=Instantaneous property of            second value (from reactor 2) before being corrected by lab            value at time ts        -   UC_(ts) ^(cor)=Update constant for reactor 2 property after            corrected by lab value at sample time ts        -   g( )=function of property in instantaneous model (i.e.            logarithmic for MI, linear for xylene solubles) applied to            corrected instantaneous property.        -   h( )=Unbiased non linear model relating reactor conditions            to resin property at sample time ts

Sometime, the controller includes two separate trajectory generators.One trajectory generator sets a trajectory for the property set point.The second trajectory generator generates a feedback trajectory for thedifference between the model and the set point. This allows the systemto control how aggressively it will respond with respect to a set pointchange independently from how aggressively it will respond to an updatefrom empirical data.

In particular embodiments, the control methodology includes determininga model bias at the start of a transition. Some such methods include notchanging the model bias at the start of a transition. Other embodimentsuse a historical model bias as saved in the recipe. In still otherembodiments, the method calculates a model bias based on expectedconditions or a relative change to the model bias is applied.

Accordingly, embodiments of the methods described herein providemodeling of polymer reactions in reactor networks and determining one ormore control actions. Particular embodiments track instantaneousproperty measures throughout the reactor network and calculatecumulative property distributions resulting from the mixing of thevarious reaction components within the reactor system.

It should be understood that the foregoing methods are executed in adigital processor of a computer system. Typically, suitable computersystems a digital processor with sufficient working memory, disk memoryand the like, and I/O peripherals common in the art including, but notlimited to, a viewing monitor, a keyboard and a mouse. The digitalprocessor may be a node or server in a network of computers

Preferably, the methods described herein are executed in the workingmemory of the digital processor with user input being received from I/Operipherals and visual output being provided on monitor. Typically, adatabase of reactor system information/data is also involved. Thedatabase may reside locally in memory or off disk or the like. Thevarious software modules may share the database information forrespective processing. In the preferred embodiment, the control methodsdescribed herein form part of a multiplicity of software modules thatseparately or cooperatively model, monitor and analyze reactor systems,including reactor networks and chemical processes/reactions performed insuch reactor networks. Such computer configurations and software modulesand architectures are within the purview of the skilled artisan.

Methods described herein can be tailored to a variety of reactor schemesand reaction types. In some embodiments, the control methods describedherein are applied in a reactor system for a continuous gas phasepolymerization reaction in a stirred or fluidized bed reactor, or for asolution polymerization process. The reactor system includes mechanismsfor altering the reaction temperature and the inflow of gases into thereactor, among other control mechanisms. In some embodiments, a lowmolecular weight component and a high molecular weight component aremade in the same reaction vessel. Some such embodiments employ a singlecatalyst that makes both the low molecular weight component and the highmolecular weight component. In other such embodiments, each component ismade by a different catalyst in the same reactor. In yet otherembodiments, the polymer can be made by combining components fromseparate reactors. For example, in a parallel reactor process, onereactor can prepare a low molecular weight component while a secondreactor can prepare a high molecular weight component and the desiredcomposition is made by combining the low molecular weight component andthe high molecular weight component in a third reaction vessel.

The polymerization may be carried out as a batch or a continuouspolymerization process. A continuous process is preferred, in whichevent catalysts, solvent or diluent (if employed), and comonomers (ormonomer) are continuously supplied to the reaction zone and polymerproduct continuously removed therefrom. The polymerization conditionsfor manufacturing the interpolymers according to embodiments of theinvention are generally those useful in the solution polymerizationprocess, although the application is not limited thereto. Gas phase andslurry polymerization processes are also believed to be useful, providedthe proper catalysts and polymerization conditions are employed.

In some embodiments, the polymerization is conducted in a continuoussolution polymerization system comprising two reactors connected inseries or parallel. One or both reactors contain at least two catalystswhich have a substantially similar comonomer incorporation capabilitybut different molecular weight capability. The final product is amixture of the two reactor effluents which are combined prior todevolatilization to result in a uniform mixing of the two polymerproducts. Such a dual reactor/dual catalyst process allows for thepreparation of products with tailored properties. In one embodiment, thereactors are connected in series, that is the effluent from the firstreactor is charged to the second reactor and fresh monomer, solvent andhydrogen is added to the second reactor. In one embodiment, the secondreactor in a series polymerization process contains a heterogeneousZiegler-Natta catalyst or chrome catalyst known in the art.

In particular embodiments, the methods are used to control a fluidizedbed process. A fluidized bed process is typically practiced by passing agaseous stream containing one or more monomers continuously through afluidized bed reactor under reactive conditions in the presence of apolymerization catalyst. The parts of a fluidized bed reaction systemtypically include a vessel, a bed, a gas distribution plate, inlet andoutlet piping, one or more compressors, one or more cycle gas coolers(heat exchangers), and a product discharge system. Typical fluidized bedreactors and procedures are described, for example, in U.S. Pat. No.6,384,157 (Cai et al.), U.S. Pat. No. 6,063,877 (Kocian et al.), U.S.Pat. No. 5,990,250 (Parrish et al., control of bed temperature), U.S.Pat. No. 5,844,054 (Samples et al.), U.S. Pat. No. 5,627,242 (Jacobsonet al.), U.S. Pat. No. 4,482,687 (Noshay et al.), and U.S. Pat. No.4,302,565 (Goeke et al.), the disclosures of which are incorporated byreference herein.

In a fluidized bed process, the product composition of α-olefin polymerscan be varied by changing the molar ratios of monomers introduced intothe fluidized bed. The resin product is continuously discharged ingranular or particulate form from the reactor as the bed level builds upwith polymerization. A gaseous stream of unreacted monomer is withdrawnfrom the reactor continuously and recycled into the reactor along withmake-up monomer added to the recycle stream, and if desired, modifiersand/or an inert carrier gas. During the course of polymerization, thebed is comprised of formed polymer particles, growing polymer particles,and catalyst particles fluidized by polymerization and modifying gaseouscomponents introduced at a flow rate or velocity sufficient to cause theparticles to separate and act as a fluid. The production rate can becontrolled in part by adjusting the catalyst feed rate. Thehydrogen/monomer molar ratio or other reactant concentrations (e.g.,comonomer feed, chain termination agent feed such as hydrogen or apoison such as oxygen) can be adjusted to control average molecularweights.

The residence time of the mixture of reactants including gaseous andliquid reactants, catalyst, and resin in the fluidized bed is generallyabout 1 to about 12 hours, and the total pressure in the fluidized bedreactor is generally about 100 to about 600 psi (pounds per squareinch). Partial pressure of the primary α-olefin is set according to theamount of polymer desired. The balance of the total pressure is providedby α-olefins other than the primary α-olefin and/or inert gases such asnitrogen and inert hydrocarbons. The temperature in the reactors isgenerally in the range of about 10° C. to about 130° C.

A stirred-tank reaction is typically practiced using a two-phase(gas/solid) stirred bed, back mixed reactor. A typical stirred tankreactor is described, for example, in U.S. Pat. No. 5,844,054. (Sampleset al.), the disclosure of which is incorporated by reference herein. Ingeneral, a set of four “plows” mounted horizontally on a central shaftin a vertical cylindrical chamber rotate to keep the particles in thereactor mechanically fluidized. A disengager vessel is mounted atop thevertical cylinder on the reactor. Gas is continually recirculatedthrough both the reactor and disengager via a blower so that the gascomposition is homogeneous throughout. Reactor pressure used istypically in the range of about 300 to about 450 psig. Partial pressuresof monomers and hydrogen (for molecular weight control) are typicallyabout 150 to about 300 psig. Gas composition can be measured at timeintervals by a gas chromatograph analyzer. The reactor is typicallycooled by an external jacket of chilled glycol to maintain a reactortemperature of about 10° C. to about 110° C. Catalyst precursor can befed either dry or as a slurry. The reactor is typically run in acontinuous mode in which granular polymer is withdrawn while thepolymerization is in progress.

A typical run in either a fluidized bed reactor or a stirred tankreactor commences with monomers being charged to the reactor and feedsadjusted until the desired gas composition is reached. An initial chargeof cocatalyst is added prior to starting catalyst feeding in order toscavenge any poisons present in the reactor. After the catalyst feedstarts, monomers are added to the reactor sufficient to maintain gasconcentrations and ratios. Cocatalyst feed rate is maintained inproportion to the catalyst feed rate. A start-up bed can be used tofacilitate stirring and dispersal of catalyst during the initial part ofthe operation. After the desired batch weight is made, the reactor isvented, and monomers are purged from the resin with nitrogen. The batchis then discharged into a box, open to the atmosphere, unless othercatalyst deactivation measures are specified.

A conventional system for conducting a solution polymerization processcomprises a single loop reactor or dual loop reactor. Flow looprecycling reactors are described, for example, in U.S. Pat. No.5,977,251 and WO97/36942 (Kao et al., to The Dow Chemical Company), thedisclosures of which are incorporated by reference herein. A flow loopreactor includes a monomer inlet, catalyst inlet, solvent inlet, and aproduct outlet, and other features including, for example, an additiveinlet, a static mixer, recycling line, and purification beds. A pumpmoves the reactant materials and polymer around the flow loop.

In such a system, monomer/comonomer and a chain termination agent can beflowed into a solvent delivered through the solvent inlet, and thenintroduced into the flow loop reactor at a monomer inlet. Catalyst andcocatalyst are combined to form a catalyst solution, a mixture withsolid activated catalyst suspended therein, or a slurry of supportparticles with adsorbed catalyst suspended in a solvent media, which isinjected or flowed through the catalyst inlet into the flow loop.Polymer is flowed out of the reactor through the polymer outlet. In acontinuous system, some of the material in the reaction stream flowscontinuously past the product outlet and back through the loop.

The polymer produced can be a polyolefin, e.g., homopolymer or copolymerof ethylenically and/or acetylenically unsaturated monomers. Suchmonomers include C2-C20 α-olefin monomers including, but are not limitedto, ethylene, propylene, isobutylene, 1-butene, 1-pentene, 1-hexene,4-methyl-1-pentene, 1-decene, 1-octene, 1-nonene, 1-undocene,1-dodecene, 1-tridecene, 1-tetradecene, 1-pentadecene, among others.Other monomers include styrene, C₁-C₄ alkyl substituted styrenes,tetrafluoroethylene, vinylbenzocyclobutene, dienes such as1,4-hexadiene, dicyclopentadiene, ethylidenenorbornene, 1,7-octadieneand 1,9-decadiene, and cycloalkenes such as cyclopentene, cyclohexeneand cyclooctene.

The various olefin polymerization reactors can be utilized and adjustedto produce a wide variety of polymer products. Exemplary polymers thatcan be produced in accordance with the invention include homopolymersand copolymers of polyethylene, polypropylene, and C₃-C₁₂ α-olefins;terpolymers of ethylene, at least one C₃-C₁₂ α.-olefin and a diene suchas ethylene-propylene-diene monomer (EPDM); polybutadiene, polyisoprene,polystyrene; and other rubbers. Generally, the polymer products made bya given reactor system use the same reactants but in different ratiosand at different temperatures. Each of these polymer products can bemade with a number of different resin properties, or grades. Each gradeof polymer product has a narrow limit on its properties, e.g., densityand melt index.

The reactors can be utilized to prepare various polymer types including,but not limited to, homogeneous polymers, heterogeneous polymers,substantially linear polymers, substantially random ethylene/styreneinterpolymers, and olefin-based elastomers.

Homogeneous linear ethylene polymers can be prepared in conventionalpolymerization processes using Ziegler-type catalysts such as, forexample, zirconium and vanadium catalyst systems, as exemplified in U.S.Pat. No. 3,645,992 to Elston, incorporated herein by reference. U.S.Pat. No. 4,937,299 to Ewen et al. and U.S. Pat. No. 5,218,071 to Tsutsuiet al., each of which is incorporated herein by reference, disclose theuse of metallocene catalysts, such as catalyst systems based onzirconium and hafnium, for the preparation of homogeneous linearethylene polymers. Homogeneous linear ethylene polymers are typicallycharacterized as having a molecular weight distribution, Mw/Mn, of about2. Commercially available examples of homogeneous linear ethylenepolymers include those sold by Mitsui Petrochemical Industries asTafmer™ resins and by Exxon Chemical Company as Exact™ resins.

Heterogeneous linear ethylene polymers are available from The DowChemical Company as Dowlex™ LLDPE and as Attane™ ULDPE resins.Heterogeneous ethylene polymers are typically characterized as havingmolecular weight distributions, Mw/Mn, in the range of from 3.5 to 4.1.Heterogeneously branched ethylene polymers are characterized as amixture of interpolymer molecules having various ethylene to comonomermolar ratios, and a short chain branching distribution index (SCBDI)less than about 30 percent. Heterogeneous polymers also have multiplemelting peaks (i.e., exhibit at least two distinct melting peaks). Allknown heterogeneously branched ethylene polymers are linear and have nomeasurable or demonstrable long chain branching. Heterogeneous linearethylene polymers can be prepared via the solution, slurry or gas phasepolymerization of ethylene and one or more optional α-olefin comonomersin the presence of a Ziegler-Natta catalyst, by processes such as aredisclosed in U.S. Pat. No. 4,076,698 (Anderson et al.) and U.S. Pat. No.5,231,151 (Spencer et al.), incorporated herein by reference.Ziegler-Natta type polymerization processes are also described, forexample, in U.S. Pat. No. 4,314,912 (Lowery, Jr. et al.), U.S. Pat. No.4,612,300 (Coleman, III), U.S. Pat. No. 5,869,575 and U.S. Pat. No.5,844,045 (Kolthammer et al.) and U.S. Pat. No. 5,231,151 (Spencer etal.) (all to The Dow Chemical Company), the disclosures of which areincorporated by reference herein.

Substantially linear ethylene polymers (SLEPs) are homogeneouslypolymers having long chain branching, and are described, for example, inU.S. Pat. Nos. 5,272,236, 5,278,272, 5,665,800 and 5,783,638 (Lai etal., to Dow Chemical), the disclosures of which are incorporated byreference herein. The term “substantially linear” means that, inaddition to the short chain branches attributable to homogeneouscomonomer incorporation, the ethylene polymer has long chain branches,such that the polymer backbone is substituted with an average of 0.01 to3 long chain branches/1000 carbons. The melt index for SLEPs isgenerally at least about 0.1 grams/10 minutes (g/10 min) up to about 100g/10 min. SLEPs are made by the Insite™ Process and Catalyst Technology,and are available from The Dow Chemical Company as Affinity™ polyolefinplastomers and from DuPont Dow Elastomers, LLC as Engage™ polyolefinelastomers. SLEPs can be prepared via the solution, slurry, or gasphase, preferably solution phase, polymerization of ethylene and one ormore optional α-olefin comonomers by a continuous process in thepresence of a constrained geometry catalyst, such as is disclosed, forexample, in European Patent Application No. 416,815-A, U.S. Pat. Nos.5,132,380, 5,189,192, 5,374,696, 5,453,410, 5,470,993, 5,494,874, and5,532,394, incorporated herein by reference.

Substantially random interpolymers can be prepared by polymerizing anα-olefin(s) with a vinyl or vinylidene aromatic monomer(s) and/orhindered aliphatic or cycloaliphatic vinyl or vinylidene monomer(s).Substantially random interpolymers are described, for example, in U.S.Pat. No. 6,211,302 (Ho et al.) U.S. Pat. No. 6,190,768 (Turley et al.),U.S. Pat. No. 6,156,842 (Hoenig et al.), and U.S. Pat. No. 6,111,020(Oriani et al.), the disclosures of which are incorporated by referenceherein. The preparation of substantially random interpolymers includespolymerizing a mixture of polymerizable monomers in the presence of oneor more metallocene or constrained geometry catalysts in combinationwith various cocatalysts. Operating conditions include pressures fromatmospheric up to 3000 atmospheres and temperatures from −30° C. to 200°C. Examples of suitable catalysts and methods for preparing theinterpolymers are described in EP 0,416,815(B1) and U.S. Pat. No.5,703,187 (Timmers), the disclosures of which are incorporated byreference herein.

An example of olefin-based elastomers is a terpolymer made fromethylene-propylene diene monomer (EDPM). A process for preparing EPMpolymers is described, for example, in U.S. Pat. No. 3,341,503 (Paige etal., Uniroyal, Inc.), the disclosures of which are incorporated byreference herein. An exemplary catalyst system for preparing EDPMcomprises a vanadium compound such as vanadium oxytrichloride ortetrachloride, a co-catalyst that is typically an organoaluminumcompound, and an activator such as a nitropropane and quinone.

Any catalyst conventionally employed to produced the above-mentionedpolymers can be used for polymerization in the process of the invention.Such catalysts can include Phillips catalysts, Ziegler catalysts,Ziegler-Natta catalysts containing transition metals such as vanadium,chromium, titanium, and metallocenes. Examples of useful metallocenecatalysts known in the art are disclosed, for example in U.S. Pat. No.5,455,366 (Rohrmann), U.S. Pat. No. 5,329,033 (Spaleck et al.), U.S.Pat. No. 5,317,036 (Brady et al.), U.S. Pat. No. 5,145,819 (Winter etal.), and U.S. Pat. No. 5,106,806 (Job), the disclosures of which areincorporated by reference herein.

Homogeneous catalysts employed in the production of a homogeneousethylene interpolymer include metallocene species based onmonocyclopentadienyl transition metal complexes described in the art asconstrained geometry metal complexes (CGC catalysts), including titaniumcomplexes. Useful metallocene species include constrained geometry metalcomplexes as disclosed in U.S. Pat. Nos. 5,869,575 and 5,844,045(Kolthammer et al.), U.S. Pat. Nos. 5,783,638, 5,665,800, 5,278,272 and5,272,236 (Lai et al.), U.S. Pat. No. 5,703,187 (Timmers), and U.S. Pat.No. 5,677,383 (Chum et al.), all to The Dow Chemical Company, thedisclosures of which are incorporated by reference herein.

Heterogeneous catalysts that can be employed include typicalZiegler-type catalysts. Heterogeneous catalysts comprise a supportedtransition metal compound (e.g., a titanium compound or a combination ofa titanium compound and a vanadium compound) and a cocatalyst/activator.Examples of such catalysts are described in U.S. Pat. No. 5,231,151(Spencer et al.), U.S. Pat. No. 4,612,300 (Coleman, III), U.S. Pat. No.4,547,475 (Glass et al.), U.S. Pat. No. 4,314,912 (Lowery, Jr. et al.),and U.S. Pat. No. 4,076,698 (Anderson et al.), all to The Dow ChemicalCompany the disclosures of which are incorporated by reference herein.

Examples of chromium-based catalysts are described, for example, in U.S.Pat. No. 4,540,755 (Mayhew et al.), U.S. Pat. No. 4,619,980 (McDaniel),U.S. Pat. No. 4,668,838 (Briggs), U.S. Pat. No. 4,735,931 (McDaniel),U.S. Pat. No. 5,066,736 (Dumain et al.), U.S. Pat. No. 5,244,987(Bernard et al.), U.S. Pat. No. 5,115,068 (Bailey et al.), U.S. Pat. No.5,137,994 (Goode et al.), U.S. Pat. No. 5,473,027 (Batchelor et al.),and U.S. Pat. No. 4,804,714 (Olivo), the disclosures of which areincorporated by reference herein. Chromium-based catalysts also includeother fluoride and titanium modified chromium catalysts and silylchromates. In a chromium-based catalyst system, oxygen can be used tomodify the production rate and resin properties, particularly the flowproperties of the resin, typically either the melt index or flow index,at a set oxygen to α-olefin molar ratio and catalyst feed rate toachieve desired resin properties and a desired production rate.

Conventional additives that can be introduced into the resin include,for example, antioxidants, ultraviolet absorbers, antistatic agents,photosensitizers, pigments, dyes, nucleating agents, fillers, slipagents, fire retardants, plasticizers, processing aids, lubricants,stabilizers, smoke inhibitors, viscosity control agents, andcrosslinking agents, catalysts, and boosters, tackifiers, andanti-blocking agents.

Various articles can be prepared from the olefin polymer productsprepared using the disclosed control methodologies. Such products can beused in injection molded, blow molded, roto-molded products, wirecoating, piping and tubing, and films. Useful articles include filmssuch as cast, blown and extrusion coated types of films; fibers such asstaple fibers, spunbonded fibers, or melt blown fiber systems (usinge.g., systems as disclosed in U.S. Pat. No. 4,340,563 (Appel et al., toKimberly-Clark); U.S. Pat. No. 4,663,220 (Wisneski et al., toKimberly-Clark); U.S. Pat. No. 4,668,566 (Braun, to Kimberly-Clark); orU.S. Pat. No. 4,322,027 (Reba, to Crown Zellerbach); and gel spun fibersystems (e.g., the system disclosed in U.S. Pat. No. 4,413,110 (Kaveshet al., to Allied Corporation), both woven and nonwoven fabrics such asspunlaced fabrics (as disclosed in U.S. Pat. No. 3,485,706 (Evans)), orstructures made from such fibers, including, for example, blends ofthese fibers with other fibers, e.g., PET or cotton; and molded articlessuch as articles made using an injection molding process, a blow moldingprocess, or a rotomolding process. The polymer products described hereinare also useful for wire and cable coating operations, shrink filmapplications as well as in sheet extrusion for vacuum formingoperations. Polymers made by these processes may also be useful for pipeapplications, such as gas and water pipes. Fabricated articles made fromethylene polymer blends comprising at least one homogeneously branchedsubstantially linear ethylene/α-olefin interpolymer and at least oneheterogeneously branched ethylene polymer, are described by Chum et al.,in U.S. Pat. No. 5,677,383. Compositions comprising olefin polymers canbe formed into fabricated articles such as those mentioned usingconventional polyolefin processing techniques, which are well known tothe skilled in the art of polyolefin processing.

While various embodiments of the disclosed method have been describedabove, it should be understood that they have been presented by way ofexample only, and not limitation. For example, while the exemplaryembodiments depict systems and methods applied in a two-reactor system,the system could be, for example, a single reactor system with twocatalysts. Thus, the breadth and scope of the invention(s) should not belimited by any of the above-described exemplary embodiments, but shouldbe defined only in accordance with any claims and their equivalentsissuing from this disclosure. Furthermore, the above advantages andfeatures are provided in described embodiments, but shall not limit theapplication of such issued claims to processes and structuresaccomplishing any or all of the above advantages.

1. A method of controlling a process for producing a polymer in at leastone reactor, comprising: (a) calculating a first value of at least oneproperty of a first polymer component using a mathematical model for thefirst polymer component produced by a first catalyst or under a firstset of reaction conditions; (b) calculating a second value of the atleast one property of a second polymer component using a mathematicalmodel for the second polymer component produced by a second catalyst orunder a first set of reaction conditions; (c) determining the relativerate of production of the first and second polymer components; (d)calculating a bulk average value of the at least one property using amathematical model for the bulk averaged composition; (e) adjusting oneor more reaction conditions thereby effecting an instantaneous value ofthe at least one property of at least one of the first or second polymercomponents or effecting the production rate of at least one of the firstor second polymer components to move the bulk average value toward adesired set point value.
 2. The method according to claim 1 including(f) determining an update factor from estimated or calculated processand resin conditions and an independent laboratory or instrumentmeasurement.
 3. The method according to claim 2, wherein the first valueof the at least one property is an instantaneous value.
 4. The methodaccording to claim 3 further including (g) adjusting the mathematicalmodel for the first polymer component using the update factor determinedor derived from empirical data.
 5. The method according to claim 2,wherein the second value of the at least one property is aninstantaneous value.
 6. The method according to claim 5 furtherincluding adjusting the mathematical model for the second polymercomponent using the update factor determined or derived from empiricaldata.
 7. The method according to claim 2, further including adjustingthe mathematical model for the production rate using the update factordetermined or derived from empirical data.
 8. The method according toclaim 2 further including adjusting the mathematical model for the bulkaveraged value of the at least one property using the update factordetermined or derived from empirical data.
 9. The method according toclaim 1 wherein the first and second polymer components are produced bya single catalyst system in a multiple reactor system.
 10. The methodaccording to claim 1 wherein the first and second polymer components areproduced by a mixed catalyst system in a single reactor.
 11. The methodaccording to claim 1 wherein the first and second polymer components areproduced by catalyst system having at least two catalytically activesites in a single reactor.
 12. The method according to claim 1 whereinthe first component is produced by a first catalyst and the secondpolymer component is produced by a second catalyst.
 13. The methodaccording to claim 1 including iteratively, periodically, orintermittently repeating steps a-e.
 14. The method according to claim 2including iteratively, periodically, or intermittently repeating stepsa-f.
 15. The method according to claim 3 including iteratively,periodically, or intermittently repeating steps a-g.
 16. A method ofcontrolling a process for producing a polymer composition, the methodcomprising: (a) determining an existing volume of a polymer composition;(b) calculating a first instantaneous value of a property and productionrate of a first polymer component using a mathematical model at a firsttime; (c) calculating an second instantaneous value of the property andproduction rate of a second polymer component using a mathematical modelat a first time; (d) calculating a bed average value of the property ofpolymer composition comprising the first polymer component and thesecond polymer component from the first and second instantaneous valuescalculated in (a), (b), and the existing volume based on a set of mixingrules at the first time, t₁; (e) implementing a control action to movethe value of the bed average property toward a desired value of the bedaverage property.
 17. The method according to claim 16, wherein thecontrol action includes affecting the instantaneous value of theproperty of the first polymer component.
 18. The method according toclaim 16, wherein the control action includes affecting theinstantaneous value of the property of the second polymer component. 19.The method according to claim 16, wherein the control action includesaffecting the relative production rates of at least one of the first orsecond polymer components.
 20. The method according to claim 16, whereincalculating the bed averaged value of the property is achieved using amixing rule according to the following formula:${\hat{P}}_{{bulk},k}^{- \frac{1}{b}} = \frac{{R_{1,k}{\hat{P}}_{1,k}^{- \frac{1}{b}}} + {f_{k}R_{2,k}{\hat{P}}_{2,k}^{- \frac{1}{b}}} + {\frac{V_{k - 1}}{\Delta\; t}{\hat{P}}_{{bulk},{k - 1}}^{{cor}^{- \frac{1}{b}}}}}{\frac{V_{k}}{\Delta\; t} + R_{{total},k}}$where: {circumflex over (P)}_(1,k)=Instantaneous Property of first valueat time k {circumflex over (P)}_(2,k)=Instantaneous Property of secondvalue at time k {circumflex over (P)}_(bulk,k−1) ^(cor)=Corrected bulkproperty at time k−1 {circumflex over (P)}_(bulk,k)=Bulk property attime k R_(1,k)=Production rate of first value at time kR_(2,k)=Production rate of second value at time k R_(total,k)=Totalrates discharged f_(k)=Model update factor at time k V_(k−1)=Volume oftotal polymer at time k−1 V_(k)=Volume of total polymer at time kΔt=Calculation interval b=Mixing coefficient.
 21. The method accordingto claim 16 wherein the first and second polymer components are producedby a single catalyst system in a multiple reactor system.
 22. The methodaccording to claim 16 wherein the first and second polymer componentsare produced by a mixed catalyst system in a single reactor.
 23. Themethod according to claim 16 wherein the first component is produced bya first catalyst and the second polymer component is produced by asecond catalyst.
 24. The method according to claim 16 includingiteratively, periodically, or intermittently repeating steps a-e.